Digital Logic

Digital Logic (Greek, logica, â€˜reasoningâ€™) is a method by which electrical circuits are provided with a limited ability to make decisions. The most common use of digital logic today is in the control and arithmetic functions of digital computers, without which modern life would grind to a halt.

Digital systems operate using discrete values to represent the information to be conveyed. The simplest example would be one in which the only permitted values were â€˜0â€™ meaning â€˜offâ€™, or â€˜1â€™ meaning â€˜onâ€™. Such as system is termed a binary system or a system having two states.

The first digital logic system applied to electrical circuits was proposed by Shannon in 1938 in America, when he applied Boolean algebra (see Boolean logic) to electrical switching circuit design. The switching circuits were a form of binary system as mentioned above. Boolean algebra allowed mathematical manipulation of logic statements such as â€˜ANDâ€™ or â€˜ORâ€™ functions. A Two-input â€˜ANDâ€™ function, for example, would only output a â€˜1â€™ or â€˜onâ€™ state if both input states were â€˜1â€™ or â€˜onâ€™. In this case it required one input and the other input to be â€˜1â€™ to produce a â€˜1â€™ on the output. Any other combination of inputs including both â€˜0â€™ or â€˜offâ€™ gave a â€˜0â€™ or â€˜offâ€™ output.

Shannon implemented this reasoning to give initially simple electrical circuits an element of decision-making. For example, a circuit could be constructed which required two switches to be in a closed state, before a lamp was lit. In such an instance the logic is inherent in the switching layout: that the lamp remains â€˜offâ€™ until both switches are â€˜onâ€™. Logic functions such as â€˜ANDâ€™ and â€˜ORâ€™ and many others, could then be physically constructed using electrical switch layouts. These switching circuits were termed logic gates.

It was soon realized that simple arithmetical tasks such as addition could be performed by implementation of the necessary logic gates, configured in a manner determined by Boolean algebra. This development led to the production of the first electrical calculators at the time of World War II.

Following inventions in other areas of electrical science, such as electronic theory and semiconductor device theory, memory units were invented using logic gates, as well as by magnetic tape drive and digital integrated circuit memory. This allowed results from arithmetical operations using logic gates to be stored and allowed computer programs to operate. (Computer programs step through a series of instructions, some of which may perform arithmetic operations using logic gates, while others may use logic gates to determine whether certain switches are â€˜onâ€™ or â€˜offâ€™ and therefore to determine whether certain conditions are satisfied.) The memory units permitted automatic operation of a program, enabling the results of logic operations to be stored and recalled whenever necessary.

The modern digital computer is the summit so far of achievement in digital logic. A computer will take an input signal and process that signal under the control of a program stored in its memory. Such programs today mean that millions of arithmetical calculations can be performed per second, feats that could not possibly be achieved by other means. AC